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Simplifying 200 = 12t + 4.9t2 Solving 200 = 12t + 4.9t2 Solving for variable 't'. Reorder the terms: 200 + -12t + -4.9t2 = 12t + -12t + 4.9t2 + -4.9t2 Combine like terms: 12t + -12t = 0 200 + -12t + -4.9t2 = 0 + 4.9t2 + -4.9t2 200 + -12t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 200 + -12t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -40.81632653 + 2.448979592t + t2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + 2.448979592t + 40.81632653 + t2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + 2.448979592t + t2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + 2.448979592t + t2 = 0 + 40.81632653 2.448979592t + t2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 2.448979592t + t2 = 40.81632653 The t term is 2.448979592t. Take half its coefficient (1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. 2.448979592t + 1.499375261 + t2 = 40.81632653 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592t + t2 = 40.81632653 + 1.499375261 Combine like terms: 40.81632653 + 1.499375261 = 42.315701791 1.499375261 + 2.448979592t + t2 = 42.315701791 Factor a perfect square on the left side: (t + 1.224489796)(t + 1.224489796) = 42.315701791 Calculate the square root of the right side: 6.505052021 Break this problem into two subproblems by setting (t + 1.224489796) equal to 6.505052021 and -6.505052021.Subproblem 1
t + 1.224489796 = 6.505052021 Simplifying t + 1.224489796 = 6.505052021 Reorder the terms: 1.224489796 + t = 6.505052021 Solving 1.224489796 + t = 6.505052021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + t = 6.505052021 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = 6.505052021 + -1.224489796 t = 6.505052021 + -1.224489796 Combine like terms: 6.505052021 + -1.224489796 = 5.280562225 t = 5.280562225 Simplifying t = 5.280562225Subproblem 2
t + 1.224489796 = -6.505052021 Simplifying t + 1.224489796 = -6.505052021 Reorder the terms: 1.224489796 + t = -6.505052021 Solving 1.224489796 + t = -6.505052021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + t = -6.505052021 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = -6.505052021 + -1.224489796 t = -6.505052021 + -1.224489796 Combine like terms: -6.505052021 + -1.224489796 = -7.729541817 t = -7.729541817 Simplifying t = -7.729541817Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.280562225, -7.729541817}
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